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arXiv:2009.12284 · Physical Review A

Reply to “Comment on ‘Physics without determinism: Alternative interpretations of classical physics’ ”

Flavio Del Santo, Nicolas Gisin

Published Sep 30, 2020• 2 citations
arXivHTMLPDF

Abstract

In this short note we reply to a Comment by Callegaro et al. [Callegaro, Pennecchi, and Bich, Phys. Rev. A 102, 036201 (2020)] that points out some weakness of the model of indeterministic physics that we proposed in our work [Del Santo and Gisin, Phys. Rev. A 100, 062107 (2019)], based on what we named ``finite information quantities'' (FIQs). While we acknowledge the merit of their criticism, we maintain that it applies only to a concrete example that we discussed in our work, whereas the main concept of FIQ remains valid and suitable for describing indeterministic physical models. We hint at a more sophisticated way to define FIQs which, taking inspiration from intuitionistic mathematics, would allow the criticisms in the preceding Comment to be overcome.

DOI
10.1103/physreva.102.036202

Related papers

Comment on “Physics without determinism: Alternative interpretations of classical physics”

Luca Callegaro, Francesca Romana Pennecchi, Walter Bich

The paper ``Physics without determinism: Alternative interpretations of classical physics'' [Phys. Rev. A 100, 062107 (2019)] defines finite information quantities (FIQ). A FIQ expresses the available information about the value of a physical quantity. We show that a change in the measurement unit does not preserve the information carried by a FIQ and therefore that the definition provided in the paper is not complete.

arXiv:2009.11709•Physical Review A•Sep 30, 2020•3 citations

Physics without determinism: Alternative interpretations of classical physics

Flavio Del Santo, Nicolas Gisin

Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name principle of infinite precision). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on finite information quantities (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem.'' We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').

arXiv:1909.03697•Physical Review A•Dec 5, 2019•102 citations

Indeterministic finite-precision physics and intuitionistic mathematics

Tein van der Lugt

In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In this thesis, we discuss some motivations for dropping this assumption, which we believe partly arises from the usual point-based approach to the mathematical continuum. We focus on the case of classical mechanics specifically, but the ideas could be extended to other theories as well. We analyse the alternative theory of classical mechanics presented by Gisin and Del Santo, which suggests that physical quantities can equivalently be thought of as being only determined up to finite precision at each point in time, and that doing so naturally leads to indeterminism. Next, we investigate whether we can use intuitionistic mathematics to mathematically express the idea of finite precision of quantities, arriving at the cautious conclusion that, as far as we can see, such attempts are thwarted by conceptual contradictions. Finally, we outline another approach to formalising finite-precision quantities in classical mechanics, which is inspired by the intuitionistic approach to the continuum but uses classical mathematics.

arXiv:2108.05735•Aug 12, 2021•0 citations

Reply to “Comment on ‘Association between quantum paradoxes based on weak values and a realistic interpretation of quantum measurements' ”

Alice M. Aredes, Pablo L. Saldanha

Seoane et al. [preceding Comment, Phys. Rev. A 111, 066201 (2025)] criticized our work [Phys. Rev. A 109, 022238 (2024)], saying that our argument that realistic interpretations of weak values lead to inconsistencies is not valid for all weak values and quantum theories. This is true. We never intended that the arguments we presented would be valid for all weak values. We believe it is clearly stated in our work that we were dealing only with the weak values related to the quantum paradoxes cited in our paper. Seoane et al. also said in their Comment that the ``general argument'' we present in our paper is formally incorrect. However, this criticism is related to the interpretation they give to the expression ``equivalent,'' which is different from the one we use. In this sense, the presented criticisms are a matter of semantics, not of physics.

Physical Review A•Jun 2, 2025•1 citation

Reply to “Comment on ‘Nonlocality counterfactuals, and quantum mechanics’ ”

William George Unruh

Stapp [preceding Comment, Phys. Rev. A 60, 2595 (1999)] has argued that my criticism of his nonlocality proof is wrong. I point out that counterfactual arguments are fraught with dangers, and that any such claim should use them in a conservative manner. A reanalysis of his claims continues to lead me to the conclusion that the nonlocality of quantum mechanics remains unproven.

Physical Review A•Sep 1, 1999•2 citations

Real Numbers Are Not the Hidden Variables of Anything

Michel Ferdinand BRUNOT

Gisin and Del Santo have argued, in a series of influential papers (2019–2023), that real numbers are the “hidden variables of classical mechanics,” on the grounds that a typical real number contains an infinite amount of information that a finite volume of space cannot store. We show that this argument rests on a fundamental confusion between a physical quantity and the number that results from its numerization. The infinite sequence of decimals of a real number is not a property of the world but the structural product of the measurement procedure: the iterated application of a standard to an independent magnitude. The generic incommensurability of any two magnitudes of the same kind suffices to generate this infinite sequence. We identify and name three nested confusions: the word–thing confusion (the word “magnitude” taken for the real quantity), the quantity–number confusion (the real quantity taken for its numerical value), and their product, the numerization confusion, through which the real disappears from both sides at once. We show that these confusions symmetrically vitiate both classical determinism and Gisin’s informational indeterminism, and sketch the consequences for the determinism/indeterminism debate.

•Aug 14, 2026•0 citations
In this short note we reply to a Comment by Callegaro et al. [Callegaro, Pennecchi, and Bich, Phys. Rev. A 102, 036201 (2020)] that points out some weakness of the model of indeterministic physics that we proposed in our work [Del Santo and Gisin, Phys. Rev. A 100, 062107 (2019)], based on what we named ``finite information quantities'' (FIQs). While we acknowledge the merit of their criticism, we maintain that it applies only to a concrete example that we discussed in our work, whereas the main concept of FIQ remains valid and suitable for describing indeterministic physical models. We hint at a more sophisticated way to define FIQs which, taking inspiration from intuitionistic mathematics, would allow the criticisms in the preceding Comment to be overcome.
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name principle of infinite precision). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on finite information quantities (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem.'' We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').
In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In this thesis, we discuss some motivations for dropping this assumption, which we believe partly arises from the usual point-based approach to the mathematical continuum. We focus on the case of classical mechanics specifically, but the ideas could be extended to other theories as well. We analyse the alternative theory of classical mechanics presented by Gisin and Del Santo, which suggests that physical quantities can equivalently be thought of as being only determined up to finite precision at each point in time, and that doing so naturally leads to indeterminism. Next, we investigate whether we can use intuitionistic mathematics to mathematically express the idea of finite precision of quantities, arriving at the cautious conclusion that, as far as we can see, such attempts are thwarted by conceptual contradictions. Finally, we outline another approach to formalising finite-precision quantities in classical mechanics, which is inspired by the intuitionistic approach to the continuum but uses classical mathematics.
Seoane et al. [preceding Comment, Phys. Rev. A 111, 066201 (2025)] criticized our work [Phys. Rev. A 109, 022238 (2024)], saying that our argument that realistic interpretations of weak values lead to inconsistencies is not valid for all weak values and quantum theories. This is true. We never intended that the arguments we presented would be valid for all weak values. We believe it is clearly stated in our work that we were dealing only with the weak values related to the quantum paradoxes cited in our paper. Seoane et al. also said in their Comment that the ``general argument'' we present in our paper is formally incorrect. However, this criticism is related to the interpretation they give to the expression ``equivalent,'' which is different from the one we use. In this sense, the presented criticisms are a matter of semantics, not of physics.
Gisin and Del Santo have argued, in a series of influential papers (2019–2023), that real numbers are the “hidden variables of classical mechanics,” on the grounds that a typical real number contains an infinite amount of information that a finite volume of space cannot store. We show that this argument rests on a fundamental confusion between a physical quantity and the number that results from its numerization. The infinite sequence of decimals of a real number is not a property of the world but the structural product of the measurement procedure: the iterated application of a standard to an independent magnitude. The generic incommensurability of any two magnitudes of the same kind suffices to generate this infinite sequence. We identify and name three nested confusions: the word–thing confusion (the word “magnitude” taken for the real quantity), the quantity–number confusion (the real quantity taken for its numerical value), and their product, the numerization confusion, through which the real disappears from both sides at once. We show that these confusions symmetrically vitiate both classical determinism and Gisin’s informational indeterminism, and sketch the consequences for the determinism/indeterminism debate.